Abstract: The authors study the Hodge theory of the exterior differ-
ential operator d acting on g-forms on a smoothly bounded domain in
R7^1, and on the half space ]R++1. The novelty is that the topology
used is not an L2 topology but a Sobolev topology. This strikingly
alters the problem as compared to the classical setup. It gives rise
to a boundary value problem belonging to a class of problems first
introduced by Visik and Eskin, and by Boutet de Monvel.
AMS Classification: 35J55 35S15 35N15 58A14 58G05
Key words: de Rham complex, Sobolev topology, Hodge theory, el-
liptic boundary value problems, pseudodifferential boundary problems
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